HDU 4996 revenge of LIS (DP)

Question link: http://acm.hdu.edu.cn/showproblem.php? PID = 1, 4996

Question: How many of the longest ascending subcolumns in the full arrangement of 1 to n are K?

Idea: for the current longest ascending subcolumn, we can record the last one worth the minimum value. Therefore, we use the 2 ^ n State to indicate which numbers are used in the current longest ascending subcolumn, And the Lexicographic Order is the smallest. After the first n-1 digits, we enumerate the numbers in the last position as each digit in [1, N] and set it to K. Then we only need to set the first [1, n-1] all the numbers in the series that are greater than or equal to K can be incremented by one.

int n,k;i64 f[22][22];i64 dp[1<<22],tmp[1<<22];int cal(int x){    int ans=0;    int i;    for(i=0;i<20;i++) if(x&(1<<i)) ans++;    return ans;}void init(){    dp[1]=1;    f[1][1]=1;    int i,j;    for(i=1;i<18;i++)    {        for(j=0;j<(1<<i);j++) tmp[j]=dp[j];        for(j=0;j<(1<<(i+1));j++) dp[j]=0;        for(j=0;j<(1<<i);j++) if(tmp[j])        {            int k;            for(k=0;k<=i;k++)            {                int tot=0;                int c[20];                int t;                for(t=0;t<i;t++) if(j&(1<<t)) c[tot++]=t;                for(t=0;t<tot;t++) if(c[t]>=k) c[t]++;                c[tot++]=k;                for(t=0;t<tot;t++) if(c[t]>k)                {                    c[t]=k;                    break;                }                int st=0;                for(t=0;t<tot;t++) st|=1<<c[t];                dp[st]+=tmp[j];            }        }        for(j=0;j<(1<<(i+1));j++) f[i+1][cal(j)]+=dp[j];    }}int main(){    init();    int T;    scanf("%d",&T);    while(T--)    {        scanf("%d%d",&n,&k);        printf("%I64d\n",f[n][k]);    }}

 

HDU 4996 revenge of LIS (DP)